Image: A police checkpoint along a road leading to the Holey Artisan Bakery, the site of a deadly attack this month in Dhaka, Bangladesh.

Bangladesh, reeling from a sudden intensification of terrorism this summer, has begun an urgent search for men suspected of building an Islamic State presence in the country and recruiting young Bangladeshis to fight in Syria and Iraq.

Bangladesh’s government has maintained that the escalating attacks there were the work of domestic terrorists supported by domestic patrons, and it has dismissed claims of responsibility from groups like the Islamic State and Al Qaeda.

But a list of 10 high-value suspects that was released this month, after the harrowing siege of a restaurant in Dhaka, tells another story.

The list includes three Bangladeshi expatriates — longtime residents of Canada, Australia and Japan — who have long been sought by the police and suspected of setting up training and recruitment pipelines for the Islamic State. A fourth man on the list vanished last year after telling his brother he planned to fight for the Islamic State in Iraq, the police said.

The most talked-about of the suspects, Tamim Ahmed Chowdhury, is believed by some analysts to act as a coordinator of the Islamic State’s activities in Bangladesh and parts of northeast India. No suspects have been arrested because some operated in countries with stronger legal protections, the police said, and others have disappeared.

The profiles of these men offer a snapshot of a militancy undergoing a metamorphosis, as links develop between domestic and international terrorist groups.

“It is possible that they have become the link, the liaison between the local militants and the transnational groups, particularly in providing strategic guidance,” said Ali Riaz, a professor of politics and government at Illinois State University. “The question is, are there more like them that we don’t know?”

Until last fall, officials openly discussed fledgling efforts by a handful of Islamic State recruiters to lure Bangladeshis to Turkey, and on to Iraq or Syria. They did not seem to pose an urgent problem for Bangladesh: The number of recruits was not large, believed to be several dozen, and officials had no inkling that they aspired to carry out domestic attacks.

“We have good intelligence about Islamic State supporters,” Monirul Islam, then the joint commissioner of the Dhaka metropolitan police, said in an interview last year. “They have confided that they want to go to Syria and participate in jihad. Not in Bangladesh. Their plan does not include anything like they would kill anyone in Bangladesh.”

He added, though, that “these boys, if they return, that is a potential threat all over the world.”

After that, the question of Islamic State involvement in attacks in Bangladesh became a matter of dispute. In September, the United States warned the Bangladeshi authorities, based on intercepted communications, that the Islamic State was preparing an attack on foreigners in Bangladesh. Shortly thereafter, two foreigners were shot, and claims of responsibility began to appear on social media accounts linked to the Islamic State.

Sheikh Hasina, Bangladesh’s prime minister, responded with skepticism and mistrust, complaining that the United States had not shared any “actionable intelligence” with Dhaka. There was little evidence of Islamic State involvement beyond claims on social media, and investigators had traced dozens of previous attacks to well-established domestic networks, including some that had been active for decades.

Attributing the attacks to ISIS, moreover, threatened the country’s all-important garment industry, which depends on annual visits from Western buyers.

After militants killed 22 people at the Holey Artisan Bakery in Dhaka this month, the government said the attack was solely the handiwork of “homegrown” militants from Jama’atul Mujahedeen Bangladesh, even though the perpetrators sent photos to an Islamic State-linked private email account during the operation.

Officials softened their position as the investigation proceeded, acknowledging in recent days that the attackers may have had foreign links, including to the Islamic State.

Now the police are seeking several suspected Islamic State operatives as possible coordinators of domestic terrorism. Among the 10 high-priority suspects are three whom Mr. Islam described last year as Islamic State recruiters.

They are Mr. Chowdhury, who is thought to have returned to Bangladesh from Canada in 2013; Mohammad Saifullah Ojaki, a professor of business administration at a university in Japan; and Abu Terek Mohammad Tajuddin Kausar, who has lived in Australia for a decade.

A senior intelligence official, who spoke on the condition of anonymity because he was not authorized to speak, said the men being sought acted as contact points between militants inside Bangladesh and organizers outside the country.

The official said that two to three dozen fighters had returned from Syria and were serving as operatives in Bangladesh. Others, the official said, had returned after receiving training in Turkey, and a third group may be training within Bangladesh’s borders.

Investigators are most interested in apprehending Mr. Chowdhury, who was identified in The Daily Star, the country’s most popular English-language newspaper, as the leader of Bangladeshi militants aligned with the Islamic State. If that is true, he is the man interviewed under an assumed name in the Islamic State’s English-language magazine, Dabiq, promising to stage bloody attacks in India, “with the help of the existing local mujahedeen.”

“Our soldiers are presently sharpening their knives to slaughter the atheist, the mockers of the prophet and every other apostate in the region,” the man said in the interview. Mr. Chowdhury left Windsor, Ontario, for Bangladesh in 2013 or some time after, at the same time as two friends who the police suspected of trying to reach Syria to fight, said Amarnath Amarasingam, a fellow at George Washington University’s Program on Extremism, who tracks jihadist fighters from the West.

Before he left Canada, Mr. Chowdhury had complained to acquaintances of harassment from law enforcement, and his radical beliefs were criticized by leaders in his mosque. Acquaintances described Mr. Chowdhury as “a nerdy kid who no one would have ever thought to take on a leadership role of any kind,” Mr. Amarasingam said.

Another suspect, Mr. Ojaki, has lived in Japan for many years. Born into a modest Hindu family in central Bangladesh, he earned a scholarship and eventually taught business administration at a university in Kyoto.

While living there, he underwent a transformation, changing his name and converting to Islam, said his father, Janardan Debnath. Mr. Debnath said the family was staggered by the news of his conversion.

“When I understood, it was like I couldn’t breathe,” he said. “I was completely stunned to see the beard. We’re Hindu people, our son’s come back with this beard. The neighbors were gossiping about it.”

He had heard from reporters that his son was suspected of participating in a terrorist network, he said. “I can’t understand what’s happening at all,” he said, breaking into uncontrollable sobs.

Other suspects, too, have fallen out of touch with their families.

Nazibullah Ansari, who had been sent to study in Malaysia, sent his brother a farewell message in January 2015 saying, “I have come to Iraq to join IS, I will not be in touch with you anymore, and won’t be coming back,” said Abul Kalam, the officer in charge at the police station in Chittagong, where a missing-persons report was filed this month.

Junnun Sikder, previously a computer science student at one of Dhaka’s elite private universities, was arrested in 2013 on suspicion of serving as a recruiter for a domestic jihadist group, the Ansarullah Bangla Team. Released on bail, he left the country for Malaysia, and has since dropped out of contact.

Another, A.T.M. Tajuddin Kausar, had left Bangladesh in 2006 to study computer science in Australia, said his mother, Tahera Begum. He fell out of touch in 2013, calling once every few months. “I never thought he would be capable of being a terrorist,” she said. “I still don’t believe it.”

Zayadul Ahsan Pintu, a journalist who has published widely on the country’s militant networks, said that apprehending the 10 suspects would allow the police to “identify the linkage, internal and external.”

Mr. Chowdhury, in particular, he said, “is the connection from Bangladesh to Syria.”

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